Modeling Geographic Behavior in Riotous Crowds · analysis. Fifth, rioting is often dangerous for...

Modeling Geographic Behavior in Riotous CrowdsPaul M. Torrens and Aaron W. McDaniel

Geosimulation Research Laboratory, Department of Geography, University of Maryland

Under some conditions, tensions among crowd members, harbored a priori or developed on site, might catalyzea crowd to riot, with dramatic consequences. We know perhaps less than we would like to about the processesthat drive rioting in crowds because they are difficult to study. In particular, we know relatively little about theinfluence of geographic behavior on rioting, although there exists a general sense that it is important. In lieu ofpragmatic avenues for studying riots, we could use simulation as a synthetic laboratory for exploration. To beuseful, simulations must be based on realistic behavioral models, but the extant science for riot modeling hasnot traditionally provided that support. In this article, we introduce a new approach to modeling riot-prone andriotous crowds using behavior-driven computational agents. We demonstrate a simulation architecture based onsocioemotional agents, modeled at atomic levels and characteristic times for riot activity, but extended withthe use of geographical functionality that endows agents with spatial perception, cognition, and action thathelps to determine where, when, how, and in what contexts and company their agency should be deployed andinterpreted. In essence, our agents are polyspatial, with the ability to adapt their behavioral geography undershifting circumstances and to differentially process geographic information from diverse sources. We illustratethe usefulness of this scheme through simulation of a varying set of scenarios for riot formation, evolution,and dissolution, as well as in exploring the interplay among different characteristics, traits, and goals of riotparticipants. Key Words: agent-based model, complexity, geographic information science, riots, spatial analysis andmodeling.

Bajo ciertas condiciones, las tensiones que se presentan entre los integrantes de una muchedumbre, en latenciao desarrolladas en el propio sitio, podrıan conducir una multitud a desbocarse en asonada, con consecuenciasdramaticas. Quizas conozcamos menos de lo que quisieramos saber sobre los procesos que alientan la asonadaen muchedumbres, por lo difıcil que es estudiar este tipo de conducta. En particular, sabemos relativamentepoco acerca de la influencia del comportamiento geografico sobre las asonadas, ası exista una sensacion generalsobre la importancia que esto pueda tener. A falta de aproximaciones pragmaticas para estudiar las asonadas,podrıamos utilizar la simulacion a tıtulo de laboratorio sintetico de exploracion. Para que sirvan de algo, lassimulaciones deben basarse en modelos conductuales realistas, si bien la ciencia actual de modelizacion deasonadas todavıa no ha proporcionado tal apoyo. En este artıculo introducimos un nuevo enfoque de modelizacionde muchedumbres propensas a generar asonadas, o de turbas ya convertidas en asonada, utilizando agentescomputacionales de orientacion conductual. Hacemos la demostracion de una arquitectura de simulacion basadaen agentes socioemocionales, modelados a niveles atomicos y en tiempos caracterizados para la accion de asonada,pero fortalecidos con el uso de la funcionalidad geografica que dota a los agentes con percepcion espacial, cogniciony capacidad de accion que ayude a determinar donde, cuando, como y en cuales contextos y companıa puedadesplegarse e interpretarse su agencia. Esencialmente, nuestros agentes son poliespaciales, con habilidad paraadaptar su geografıa conductual bajo circunstancias cambiantes y para procesar diferencialmente la informacion

Annals of the Association of American Geographers, XX(XX) XXXX, pp. 1–27 C© XXXX by P. Torrens and A. W. McDanielInitial submission, April 2009; revised submissions, June and August 2011; final acceptance, August 2011

Published by Taylor & Francis, LLC.

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Sticky Note

Torrens, P.M. & McDaniel, A. (2013) “Modeling geographic behavior in riotous crowds”. Annals of the Association of American Geographers, 103(1): 20-46 (DOI: 10.1080/00045608.2012.685047)

2 Torrens and McDaniel

geografica proveniente de fuentes diversas. La utilidad de este esquema la demostramos a traves de la simulacionde un variado conjunto de escenarios para la formacion de asonadas, su evolucion y disolucion, lo mismo queexplorando interacciones entre las diferentes caracterısticas, rasgos y metas de los participantes en la asonada.Palabras clave: modelo basado en agente, complejidad, ciencia de la informacion geografica, asonadas, analisis espacial ymodelizacion.

Up rolls a riot van and sparks excitement in the boys. But thepolicemen look annoyed.

—Arctic Monkeys (2006)

Riots are just one possible outcome of human as-sembly, but they are incredibly significant. Theycan catalyze positive social dynamics, but if ri-

ots turn seditious, the consequences can be less thandesirable (McPhail 1994). Riots are difficult to studyfor a number of reasons. First, many types of riot-ing are possible, with different motivations, dynamics,and outcomes (Haddock and Polsby 1994). These in-clude food riots due to resource shortages (Auyero andMoran 2007), social riots driven by inequality or in-justice (Jackman 2002), protest riots that might beginwith peaceful demonstration (McCarthy, Martin, andMcPhail 2007), police riots challenging authority (R.Stark 1972), or hooliganism following antisocial behav-ior (Buford 1991). These distinctions are also elastic(McPhail and Wohlstein 1983), making them difficultto distinguish. Second, interpretation of rioting is al-most necessarily subjective: What might be experiencedas a collective assembly by participants could appear asa riot to another observer. This creates complicationsin characterizing riot processes. Third, rioters are un-reliably available for standard qualitative inquiry suchas surveys or interviews, making the collection of em-pirical data during riots problematic (Sampson 1999).Even analysis by pattern recognition in video footage isdifficult (Wohlstein and McPhail 1979) and might pro-vide little insight into motivations and intent of riotparticipants anyway (Prentice-Dunn and Rogers 1982).Fourth, secondary data can be unreliable and biased(Myers and Caniglia 2004), which hinders vicariousanalysis. Fifth, rioting is often dangerous for partici-pants and experimentation with real people—even ina controlled setting—is often infeasible (Kroon, VanKreveld, and Rabbie 1991).

Computer simulations could provide complementaryopportunities for studying rioting in a synthetic labora-tory, if they can be usefully allied to theory, and this isan idea that we promote in this article. We are not thefirst to think of the idea, but our approach is novel. Webelieve that geography can offer significant insight into

riot dynamics and we introduce a more authentic ge-ographic representation of riot dynamics than existingmodels have considered. We argue that this significantlybroadens the diagnostic ability of riot modeling.

Our approach incorporates several innovative fea-tures. First, we include a cross-disciplinary substantivefoundation that accommodates traditional ideas aboutrioting from sociology, psychology, and criminal justice.These ideas are realized as model behaviors that de-termine and animate synthetic rioters’ internal driversand their interactions with the social, emotional, andphysical environment developing around them. Sec-ond, our agents are endowed with rich geographic func-tionality that envelops their socio-psychological oper-ability, casting it in spatiotemporal context. This is donepolyspatially, such that agents can extensibly configureand use geographic behavior, becoming dexterous intheir interaction with geographic information, acrossscales and contexts. Third, we built our model fromthe bottom up, which enables us to design, assemble,run, and control a riot—as a simulacrum (Baudrillard1994)—in much the same way that a riot manifestsin the real world. This allows us to flexibly experimentwith different designs and characterization of syntheticrioters and varying scenarios. Fourth, we introduce anovel coupling of agent–automata models, space–timegeographic information systems, spatial analysis, spatialstatistics and geostatistics, and geovisualization as an in-tegrated pipeline for designing, running, and evaluatingexperiments about riot dynamics.

The article is organized as follows. We discuss linksbetween geography and rioting in the next section. Wethen examine existing approaches to riot modeling. Ourmethodological contributions beyond this foundationare presented following that. We then introduce exper-imental simulation scenarios and discuss results aheadof our concluding remarks.

Geographical Perspectives on Rioting

The psycho-sociological processes underpinning ri-oting are reasonably well covered as theory (Firestone1972; Haddock and Polsby 1994), but geographic pro-cesses have received less attention. Although it is un-derstood that geography plays a significant role in riot

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Modeling Geographic Behavior in Riotous Crowds 3

dynamics, this is usually only explored anecdotally inthe theoretical literature.

Riots often manifest with significant spatial patterns.Existing investigation of this topic has emphasized thecoarse patterning of rioting at the city scale (Adams1972; Berk and Aldrich 1972; M. J. A. Stark et al.1974; Carter 1986), but fine-resolution motifs of riotouscrowds are often overlooked, despite a need to betterunderstand interactions at this scale (McPhail 1994,2008). Beyond the observational work of Wright (1978)over thirty years ago, little fieldwork has been done toinvestigate the genesis or effects of riot patterns withincrowds.

Spatial interaction is a logical catalyst for rioting:people interact with each other over space and timein riotous crowds (socially, physically, verbally, and,increasingly, digitally; Marx and McAdam 1994;Rheingold 2002). Riots can also be influenced bydiffusion processes: Rumor, panic, calm, and aggressioncan spread through riots by interaction over space andtime, with individuals as vectors for their transmission(Myers 2000). The popular emphasis on the crowd—asa unit of concern—in much of the existing litera-ture, however, sidesteps consideration of intracrowdinteraction (McPhail 1994).

Scaling can also shape riot dynamics, for example,when local incidents catalyze wider response (Jacobs1996). Spatial complexity is a related consideration.Scaling in crowd behavior is often mediated by com-plex phenomena such as feedback, emergence, path de-pendency, and self-organization, each of which rely onsystem scaling (Vicsek 2001, 2003). Relatively littlehas been done to explore the role of scaling in riotphenomena; indeed, most studies have settled on a sin-gle (usually coarse—the city) scale in analysis (Abuduet al. 1972; Adams 1972; Carter 1986; DiPasquale andGlaeser 1998).

Geographic behavior is also significant in explainingriot dynamics. Some geographic behaviors might pre-empt a riot: unlawful assembly, routs, collective locomo-tion of strangers, or loitering of groups in certain placesand times, for example (McPhail and Wohlstein 1983).Police behavior amid rioting is usually geographical.This has been documented at the city scale (Yarwood2007) but is also important within crowds (Prati andPietrantoni 2009). Police can divide a crowd spatiallyto minimize the spread of rioting or might corral riotingcrowds into spaces that can be more effectively policedor where they can minimize contact between rioters andnonrioters (Newman 1972). Spatial cognition is a cru-cial component in riot behavior. People’s perceptions

of ambient conditions in riotous crowds (Felson 1982)and shifts in their mental maps amid confusion couldalter their behavior (Mawson 2005). Law enforcementcould target directly rioters’ spatial cognition by pro-jecting or inflating an impression of impending force us-ing particular collective movement strategies (Prati andPietrantoni 2009); by disrupting rioters’ spatial cogni-tion with aerosols; by blocking line of sight; or by inter-fering with their spatio-aural perception (Waddington1991). Although geographic behavior is recognized inthe literature as being important, the detailed behav-ioral interplay between individuals and within crowdshas not been investigated in sufficient detail, despitecalls for focus on the topic (McPhail 1994).

Physical geography is also important to rioting. Riotsmight originate in places and times with significanthistorical geography (Haddock and Polsby 1994).Some built environments might be temporarily orpermanently modified to reduce the physical substratefor rioting, using barricades and fencing, by designatingsanctioned time geographies for demonstration, bycharting routes for protesters to march along, or by in-stalling surveillance equipment as a deterrent (Newman1972). These ideas, although very relevant for un-derstanding riot geography, have not benefited fromthorough examination. Even Newman’s famous workfocused largely on architecture, rather than people.

Existing Riot Models

In the absence of tangible testing grounds for rioting,computer simulation can be used as a virtual laboratory.The theory needed to explain riot dynamics is relativelyunderdeveloped, however, and model builders, lackingobvious starting points for development, have tendedin the past to bend models designed for other purposesto fit riot behavior.

The majority of riot modeling work has been de-veloped for research of operations other than war(OOTW), whereby models of noncombatant crowdsare infused into military simulations for the purposesof evaluating plans and strategies (Lauren and Stephen2000, 2002; Yiu, Gill, and Shi 2002; McKenzie et al.2004; Petty et al. 2004). Not all riots are related to mili-tary activities, however, and socio-geographic dynamicsare not often a main concern.

Another thread has developed in political studies,with focus on civil violence using game-theoretic mod-els. Game-theoretic approaches carry some limitingassumptions, however, such as rational actors, perfectinformation, and simple rule-of-thumb heuristics for

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behavior (e.g., tit-for-tat or winner-takes-all). TheBrookings Model of Civil Violence (J. Epstein 2002) isa popular example of this work.

Riot-like models have also been built in physics,because of curiosity about apparent correlationsbetween social behavior and continuum mechanicsof physical particles in constrained spaces (Vicsek2003). Continuum models are useful for representingaggregate flow and crowd turbulence in confined spaces(usually conduits like stream channels or pipes), butthey do little to accommodate realistic human behavior(Treuille, Cooper, and Popovic 2006). Nevertheless,many continuum models have been ported directly toriot modeling (Kirkland and Maciejewski 2003; Bhatand Maciejewski 2006; Pabjan and Pekalski 2007).

Another thread of riot models has been developedin sociology, mostly to represent psychology of socialsignaling in collective action, using artificial intelli-gence (McPhail, Powers, and Tucker 1992; McPhail1994; Tucker, Schweingruber, and McPhail 1999).These types of models tend to emphasize individualdecision making rather than intrapersonal interactions(McPhail 1994).

Generally, geography (and particularly geographicbehavior) has received only cursory attention in mostriot models. This is especially evident in representationof movement. Although long understood to be crucialin rioting (McPhail and Wohlstein 1986), movementis often relegated to random hopping between roundsof game-theoretic exchange (Yiu, Gill, and Shi 2002)or abstract representation using physics of particle flow.For example, the J. Epstein (2002) model treated move-ment by random picking up and dropping off of agentsin cellular lattices. The model developed by Goh et al.(2006) actually relied on Conway’s mathematical ruleset for the Game of Life (Gardner 1970) for movement(this is just nonsensical; the Game of Life was built totest the computability of self-replication and has noth-ing to do with movement; Faith 1998).

The determination of neighborhoods of interactionis also weak in most riot models and this is anothertell-tale sign of shortcutting in modeling movement.A majority of riot models use cellular automata forspatial interaction, which often limits agents’ (really,cells’) activity to fixed, symmetric rasters (Torrens2009). Dibble and Feldman’s (2004) graph-based agentmodels focused admirably on the social network spaceof riot participants but lacked locomotion (in fairness,their models were designed to test graph-networkapproaches, not movement). Considerable overhead isrequired to infuse mathematical models with realistic

geographic behavior and so the diluted treatment ofgeography in existing riot models is understandable butdisappointing.

A New Approach to Riot Modeling: OurMethodology

Motivated not only by a desire to build on thework we just discussed but also to broaden therange of questions that would be posed in simulation,we introduce an innovative modeling infrastructure forriot dynamics by infusing added realism. Geography is aparticular focus of our efforts, but the model is flexible sothat a variety of social, physical, or psychological model“engines” could be embedded within the frameworkthat we provide. Indeed, we demonstrate how thisis possible, by taking the popular J. Epstein (2002)conflict model as the engine for socioemotional agencyand “wrapping” it with geographic functionality thatmobilizes that agency through simulated perception,cognition, spatial interaction, way-finding, steering,and locomotion. The resulting polyspatial agents thenbecome the building blocks for theory-driven riot sim-ulations. Their geographic functionality also enablessecond-order geographic processes, such as spatialinteraction, diffusion, scaling, spatial self-organization,and patterning to be derived from those primitives.Agents’ dynamics in simulation are not scripted; rather,they are processed or computed from a model thatdetermines their behavior given agent characteristics(states) and algorithms (rules) that feed on agents’ en-dogenous attributes; the shifting social, emotional, andphysical conditions that unfold around them; and theevents that they choose to interact with. Any resultingriot processes or phenomena are then derived (we couldsay “emerged”) directly from these synthetic behaviors.

Agent-Based Crowds

We use an agent–automata architecture for ourmodel (Turing 1950), with several advantages.Agent–automata can be represented atomically anddriven autonomously at individual scale and charac-teristic time. This helps to overcome problems of eco-logical fallacy and modifiable areal units (Openshaw1983; Wrigley et al. 1996), by improving fidelity. Char-acteristic timing allows agents to be represented withtrue temporal dynamics, avoiding the need to rely oncomparative snapshots as a proxy for temporal contin-uum (again, coarse representation is the standard ap-proach). This is particularly valuable when dealing with

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dynamic crowds, where we might be keenly interested insubtle temporal differences in behavior and outcomes,small deviations from spatial and temporal regularitiesor norms, or serial effects in the space–time continuumof processes.

Agent–automata can be fashioned as perceptivecreatures, with ability to reason about their surround-ings. Agents can be given bounded rationality: Their in-formation about the conditions unfolding around themmight not necessarily be complete and they might actsolely on the information they have on hand (in con-trast to standard approaches in game theory, for exam-ple). This is useful for representing forces of bias andeven subterfuge in riotous crowds (Prentice-Dunn andRogers 1982).

Agents are communicative: They exchange informa-tion by passing state descriptors. This can be significantwhen representing information diffusion in riot phe-nomena (Myers 2000; Rheingold 2002). In our model,we focus on nonverbal communication, which is a topicwith considerable currency in the literature (McPhail1994).

Automata are not inherently mobile in their origi-nal design (although the information that they containcould be). Lending agents locomotive abilities enablesthe modeling of pursuit, avoidance, dispersal, and chas-ing behavior, each of which are understood to factorinto rioters’ behaviors (Haddock and Polsby 1994).

Using the Epstein Model to Provide SocioemotionalAgency

We used J. Epstein’s (2002) conflict model as thesocioemotional core of our model. Although Epstein’smodel actually deals with civil violence, it provides aparsimonious treatment of socioemotional agency thatwe can (re-) use. It is important to stress that we havedeveloped significant additional infrastructure aroundthis foundation by wrapping it with geographic func-tionality and that we subsumed the algorithms for themodel (not the software) in our pipeline. Coupling di-verse agent-based models (Rank 2010) and spatializ-ing nonspatial agent behaviors (Torrens and Benenson2005) is an active topic of research in the simulationcommunity.

Following J. Epstein (2002), we consider four classesof agent-actor in simulation; Civilian, Rebel, Jailed,and Police. Agents can transition between these rolesas their agency dictates, Civilian ↔ Rebel → Jailed→ Civilian. Rebel agents that are apprehended be-come Jailed agents. (We realize that the term rebel has

significant connotations, but we use it here to simplydistinguish members of the crowd that act out an inter-nally held grievance.) Police agents are also introduced,but Civilian and Rebel agents cannot transition to lawenforcement roles and Police agents cannot be seducedto riot. These four classes provide a minimal but satis-factory set of protagonists and match standard distinc-tions in related models (Lauren and Stephen 2000; Ling2001; Yiu, Gill, and Shi 2002; Kirkland and Maciejew-ski 2003; Petty et al. 2004; Bhat and Maciejewski 2006;Goh et al. 2006).

Socioemotional State Descriptors. Agent state-descriptors are bundled to produce a socioemotionalprofile for actors in simulation. States are dynamic; theycan change as agents exchange information and act, re-act, and interact in simulation. Bundling is organized asfollows.

Ssocioemotional = {H, L , G, R, P , N}∀ Civilian andRebel agents,

where

⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

H = [0, 1]

0 ≤ L ≤ 1

G = H(1 − L)

P = 1 − exp(−k C

Av)

N = RP

(1)

J. Epstein (2002) did not provide much theoretical jus-tification for states in his original model, but we havecarefully considered this in our design. (Coincidentally,the states that Epstein proposed represent the dominanttheoretical arguments in riot research well.) Members ofriotous crowds might act out when they reach extremesof unhappiness (Prentice-Dunn and Rogers 1982), sowe lend agents an internal sense of hardship (H). H =1 when agents feel suffering and H = 0 when they donot. Rioters usually direct their discontent at somethingor someone (Firestone 1972), so in simulation citizen(non-police) agents are equipped with a sense of le-gitimacy (0 ≤ L ≤ 1) toward authority, represented onthe ground as police (Gillham and Marx 2000), rangingfrom an absence of respect for authority (L = 0) to am-bivalence (L = 0.5) and unequivocal support (L = 1).Agents’ feelings of legitimacy are an endogenous char-acteristic. As rioters might wish to keep feelings hiddenfrom police, we represented Civilian agents’ outwardaffect with a grievance level, G = H(1 – L). Althoughcitizen agents might feel complete dissatisfaction withtheir lot in life or with authority, their propensity to acton those feelings is tempered by an appreciation for the

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consequences of action (Milgrim 1964; McPhail andWohlstein 1983). This is introduced as risk-taking insimulation (R) and a calculation of the net cost–benefitof acting out (N). This calculation (per agent) balancestolerance for risk, the safety in numbers of like-mindedcitizens in the crowd, and the local presence of author-ity, N = RP (this is synonymous with the “gaming” cal-culation of relative cost introduced by Berk 1974). Thestate P = 1 − exp

(−k CAv

)is the probability of capture

per agent, where A is the number of Rebel agents andC is the number of Police agents. V defines how far Po-lice agents can see; this is essentially an arrest filter perPolice agent. J. Epstein (2002) originally used a Mooreneighborhood (a fixed-size, nonmobile, symmetric fil-ter) to poll states in his cellular automata model; wehave extended this concept considerably. Finally, K isa scaling term used to ensure plausible values of P forvalues of A = 1 and C = 1. A value of P = 0.9 is usuallyreasonable (J. Epstein 2002).

Enabling Dynamically Shifting Attitudes and Emo-tions. Transition rules control state dynamics by al-lowing agents to obtain behavioral access to states (theirown and those of other agents) and by providing agentswith the ability to process that information for theirbehavior. An activation rule determines shifts in de-meanor (which is a metastate) from Civilian to Rebel;that is, the decision to riot.

Activati on

={

Civiliant → Rebelt+1 if its [H(1 − L) − RP] > T

Civiliant → Civliant+1otherwise(T = 0.1) (2)

Activation includes a user-defined parameter (T) thatcontrols the threshold for acting out (Granovetter1978).

Police agents’ arrest behavior is described by an arrestrule:

Arrest

={

Rebelt → Jailedt→ jmax if Rebelt ∈ Vt and is selected

Rebelt → Rebelt+1otherwise (3)

Selection was random in Epstein’s model, but we addedfunctionality to make it guided, targeted, or weighted.jmax is user-definable and determines the length of Jailedagents’ incarceration. Jailed agents are removed fromthe simulated space and are essentially stripped of theiragent rights while incarcerated and are not eligible forstate-exchange or transition over time (t→jmax).

Extending Epstein Agents: Introducing GeographicBehavior

The preceding characterization is sufficient forgenerating emotional interplay between agents. Weextended this scheme by empowering agents withgeographic functionality that wraps around their so-cioemotional agency to determine how, where, when,and in what company and contexts those agenciesshould be deployed or interpreted (Figure 1). We specif-ically bestowed agents with polyspatial behavior thatallowed them to flexibly and intelligently deploy spatialcognition, vision, collision-detection heuristics, spatialtargeting, way-finding abilities, locomotion, physicaland affective steering, and the ability to develop and ap-ply spatial biases, tactics, and strategies. This representsa considerably richer and more authentic geographicalfunctionality than is usually presented in existingmodels. These behaviors are detailed individually asfollows and the algorithmic procedure for integratingthem in run time is presented in Algorithm 1.

Algorithms

Algorithm 1: pseudo-algorithm for behavioral geography updateand information flow order

1 Initialize simulation scenarios2 Assign initial (temporary) headings and directions using

random values within each agent’s vision3 Check to see if weightings need to be applied (user-defined)4 If weights are required, calculate affective targeting5 List relevant agents within vision6 Cull obscured agents7 Target the closest remaining agent (if any remain)8 Calculate vector to or away from target9 Calculate magnitude of vector10 Determine new position11 If new position is occupied, return to (3)12 Detect collisions

a. Look toward your directionb. Cast a vision ray using user-defined distancec. Reel in the vision rayd. Catalog potential collisionse. If no collisions are within movement range, proceed to

(13)f. If collisions are within movement range, perform brief

random walk and return to (a)13 Move14 [For arrest, if agent is within user-defined capture

threshold, arrest]

Improving Agents’ Geographical Perception ofTheir Dynamic Surroundings. A first step in buildinguseful geographic behavior is to provide agents with re-alistic spatial perception of events around them. In most

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Figure 1. Schematic overview of the docking of socioemotional agency with behavioral geography.

riot models, a cellular automata (CA) neighborhoodfilter is used. This is a fixed and symmetrical grid thatis homogeneously projected around each agent (Tor-rens 2009). Usually, neighborhood sizes and shapes arenot differentiated. Fixed CA neighborhoods are prob-

lematic because they are unrealistic: They lack direc-tionality and they allow people to literally have eyesin the back of their heads; they also tend to over-specify the amount of spatial interaction in a system(Torrens 2011). Instead, we use synthetic vision: Per

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Figure 2. An agent-actor (yellow) examines its neighborhood and identifies other entities that fall within its visual filter, focusing on theentity that is closest (red). The agent-actor could also use its mental map to prioritize entities that it encounters in its environment (e.g., awandering hippopotamus). (Color figure available online.)

agent awareness of the environment is (uniquely) pro-jected within a visual field (Figure 2). Returned data arestored as a mental map and this provides the informa-tional substrate for subsequent behavior.

Vision (Ft) is cast as a sector with origin at the cen-troid of an agent’s footprint. Casting is projected in aforward direction along the unit vector of the agent’sdirection of travel (at ), so that it is tight-coupled toagents’ movement. Sizing and shaping of agents’ vi-sion is determined by user-defined parameters for ra-dius r (line of sight) and angle θ (field of view), butthese can also change dynamically or algorithmicallyin run time as needed (Ft − 1

2r 2t θ t ). The radius of the

sector is also tempered with a user-defined velocity-decay parameter −α that discounts longer values of r(as r-a) when an agent is moving relatively quickly, en-abling agents’ visual appreciation of their surroundingsto be elastic. Police agents can only apprehend Rebelagents when they are physically close to them. An ad-ditional test is added to the Police’s vision to allowthem to evaluate whether their target Rebel falls withina user-defined distance threshold. Agents also usetheir vision to check whether objects are obscured, byray-casting.

Way-Finding. Before agents move, they need todecide where to go. We achieve this with synthetic way-finding by targeting. Agents use their vision to catalog

their surroundings and then they prune this informa-tion by targeting specific relevant things in their vision;targets then serve as way-points for subsequent steeringand locomotion behaviors.

In the absence of a specific target, agents move by pur-poseful milling. We provide them with a quasi-randomfeed of way-points within their vision. This producessmooth movements through incremental course cor-rection as agents’ displacement is constrained withintheir visual field over (t → t+1). Note that this is nota mathematical-style random walk, where agents couldperform instantaneous about-face maneuvers withouthaving to slow down and correct their steering first.Way-finding can also be tenacious. For example, thelocations of Rebel agents become targets for the Po-lice, allowing them to patrol the streets literally lookingfor Rebel agents to apprehend. Similarly, Rebel agentsmight target nonrioters as recruits to their cause.

Way-finding is resolved as follows. First, an agentchecks its vision for the presence of other entities, mem-orizing their locations. It identifies agents that it wishesto target, by checking its affect toward them. The agentthen uses ray-casting to determine whether any of thecandidate entities is obscured. What remains is a subsetof entities that are not obscured and that are affectivelyrelevant. The target agent that is closest to the observ-ing agent in this set is then selected as the target (in thecase of a distance tie, for example, between Rebel and

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Civilian or between Police and Civilian, the Civilianis made the target). Although agents collect all of theinformation that they see in their surroundings, they fo-cus their behavior and processing only on a single entityat a time. This is realistic given the small space–timegeographies in our model, which run at scales of asingle footstep. It is also relatively efficient compu-tationally, avoiding unneeded querying. Moreover,this approach allows us to avoid unrealistic averagingartifacts common in many potential-based models,which might cause an agent to cancel out conflictingpush–pull influences in its neighborhood and justremain in situ or float like a rudderless boat along aprevious vector (Helbing and Molnar 1995; Treuille,Cooper, and Popovic 2006).

Steering and Locomotion. Ready with a decisionabout what to do, agents actually move by steering andlocomotion. Despite the significance of collective loco-motion in rioting (McPhail and Wohlstein 1986), thisfunctionality is generally not provided in existing riotmodels and its absence really cripples agents, depriv-ing them of means to move relative to other things orpeople in simulation.

We allow agents to physically steer within crowds,and we allow them to steer emotionally, by consideringtheir affect relative to a target. Agents’ mental mapsprovide the vectors of visible targets, so an agent cancompare its own vector to the target and it can adjustits speed and steering to adopt a trajectory that inter-cepts or avoids the target (Figure 3). Vectors for the

pursuer (a) and target (b) are considered between twopoints in space (a0, a1) and (b0, b1), respectively. Weconsider only two-dimensional vectors, (a = [ax

ay]) and

(b = [bxby

]) (where ax is the position of a in the x-axisand ay is its position in the y-axis ∈ R2). Directions forthese vectors are obtained by normalizing them suchthat (a = a

|a | = 1) and (b = b|b| = 1). The velocity of

the vectors is taken as the first differential of their po-sitions (a0, a1) and (b0, b1), respectively: a =lim

�t→0�a�t

and b =lim�t→0

�b�t . When a pursuer seeks out a target, it

calculates an intercept vector c, (c = a − b) by vectoraddition. The steering vector for pursuer a to chase andintercept b is then (d = c − a) by vector subtraction.

We also introduce differential effort so that agentscan move relatively quickly or slowly, as they need. Thesteering vector of pursuit is [d = (c − a)amax ] when achases b with maximum effort. Here, we overload thenotation d for consistency with the notation of relatedvectors in Figure 4; this d should not be confused withthe distance d of the ray cast in Figure 2. Vectors forfleeing with maximum haste are taken as the inverseof seek vectors; that is, [−d = −((c − a)amax )]. (Notethat vector calculations are computed in simulation.The notation for the equal sign therefore representsan algorithmic assignment function of variables andparenthetical statements denote the logical order inwhich the algorithmic methods are assessed.)

Proactively Detecting and Avoiding Collisions.To effectively actuate their behavior in busy crowds,

Figure 3. Steering behavior for pursuit or evasion of a target. A pursuer targets another agent and might adopt a steering vector to pursue orflee that target.

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Figure 4. Ray-casting for collision detection anddepth perception. A ray is cast in the direction ofa and it is successively shortened in the directionof the agent-actor until d ≈ 0.

agents often need to preemptively avoid or pursue thingsthat they see or take an interest in. Existing riot modelsrarely treat even rudimentary geographic behavior ofthis kind.

We introduce collision detection using modifiedray-casting (Roth 1982; see also Figure 4). This al-lows each agent to project its movement vector by auser-defined magnitude |d t ′ | and to deploy the pro-jection as a sensor. For collision detection, we takethe time step (t → t + 1) and subdivide it intosmaller subincrements nested within (t → t + 1), suchthat [(t ′ → t ′ + 1 → . . . → t ′ + �t ′) ∈ (t → t + 1)].The temporal length of (t ′ → �t ′) is related tothe spatial length of (|d t ′ |). The cast ray is iter-atively shortened at the far end of its projection(0 ≈ |d t ′+�t ′ | < · · · < |d t ′+2| < |d t ′+1| < |d t ′ |) until itapproaches zero distance from the agent’s position cen-troid. At each increment of t ′, the ray is checkedfor interruption by moving or fixed objects. If a col-lision is determined, the agent will halt movement over(t → t + 1), either giving the moving object time topass by yielding or giving the other movement rulesin the agent’s behavior an opportunity to determine adiverted path around the obstacle. For fixed obstacles,the agent “retracts” the cast ray to a location just freeof collision and uses this as a target for flee behavior.

Affective Movement. A set of weights is intro-duced per agent to accommodate agents’ affective bi-ases in movement (Willis, Gier, and Smith 1979). At asimple level, weighting affords agents greater interest inrelevant objects than in irrelevant objects, but it also di-

rectly couples emotional perception to movement, per-mitting the parameterization of goal-driven strategiesand tactics. We borrowed the idea of weighted interac-tion influence from Yiu, Gill, and Shi (2002), who usedweights in their civil violence model to control infor-mation exchange in CA neighborhoods. Our approachis distinct, however, as it is specifically adapted for mo-bile, dynamic, sociospatial weighting of agent move-ment vectors. The weights are user-defined, allowingfor the influence of varying strategies to be explored insimulation.

Rebel agents’ affect is controlled by λ, which pro-vides a user-defined balance of emotional affordancethat might see-saw between Police and Civilian agents;Police agents are guided by µ, the relative trade-off be-tween Rebel agents and Civilian agents. λ is calculatedfor Rebel agents as follows.

For Rebel agents, (−WPolice + WCivilian = 1) and

= −WPolice

WCivilian, where − 1 ≤ WPolice ≤ 0 (4)

Users can adapt Rebels’ relative weighting by con-trolling WPolice (the weight that Rebel agents lend toPolice agents in their local surroundings). For example,if a simulation user tips the scale to a value of WPolice =−0.5, then WCivilian = −0.5 and λ =1, which producesan ambivalent affect for Rebels relative to Civilians andPolice. If the value of WPolice = −0.7, then WCivilian = 0.3and = 2.33, which produces a strongly negative affectfor Rebels, affording them a strong aversion to the Po-lice.

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Another weight (µ) is introduced for Police agents,as follows.

For Police agents, (WRebel + WCivilian = 1) and

µ = WRebel

WCivilian, where 0 ≤ WCivilian ≤ 1 (5)

µallows Police agents to trade-off affect relative toRebel and Civilian agents. It is controlled by adjust-ing the value of WCivilian. Preference is given to Civilianagents in the event of a tie for λ and for µ.

When a pursuer identifies a target (e.g., a Police agentidentifies a Rebel agent to arrest), it calculates an inter-cept vector in unit form and then assigns (through algo-rithmic update) a magnitude to that vector based on theresult of its weighting calculation; that is, |d| = (d + λ)for Rebel agents and |d| = (dµ) for Police. This mim-ics affective movement as it occurs in the real world;for example, when people steer to avoid undesirable en-counters on a street or move to avail of an interveningopportunity (Dabbs and Stokes 1975).

Coming Unstuck, if Necessary. On the rare occa-sion that agents become stuck in situ, they divert theirmovement behavior:

at+21 = (at ± e) , IFF the agent’s position remains

< a0,t → a0,t+1 → . . . → a0,t+20 > (6)

In Equation 6, a is an agent’s original vector(

−→a0a1). If an agent stays in situ for twenty time steps

(t → t + 1 → . . . → t + 20), it is nudged into motionagain at t + 21 with e, a random vector that sets anagent on a slightly new course with a small user-definedmagnitude and random direction e = a.

A Note on Timing. Timing is handled pseudo-synchronously (Bengtsson and Yi 2004), using memorybuffering to update agents’ information collection andtransition. One time step resolves a complete synchro-nization of all agents’ transition processing with theinformation they have for that time step (Algorithm1). The timing for this is, of course, artificial becauseit is simulated, but it is set to be roughly equivalentto a real-world second (based on plausible velocity foragents relative to real-world people). The simulationwill often run much faster than life on a computer, butin the results that we present, the relative timing is as wehave just described. (The timings and synchronizationcan be altered.)

Experimenting with Riots in Simulation

We devised four sets of scenarios to explore riotouscrowd dynamics in simulation (the parameters for eachscenario are listed in Table 1). Two scenarios were de-signed to establish base conditions in simulation:

� Base, in which 1,000 modeled agents were endowedwith what will then serve as default characteristicsand were placed in a plaza-type setting, as mightbe found in central cities or around monument in-frastructure. These types of spaces are often chosenfor collective assembly (Newman 1972; McPhail andMiller 1973). Fifty police agents were deployed to thecrowd, to represent police units that might be calledto oversee a demonstration (Earl and Soule 2006).

� Built environment, in which 285 agents were placedin a smaller urban setting with built infrastructure.This provided a simple test of the influence of thebuilt environment on riot dynamics: Agents had tonegotiate and move around built infrastructure and itinfluences their ability to acquire information aboutthe events around them. Fifteen police were intro-duced, as might be found on foot patrol.

The second set of scenarios was used to explore riot-ing from the perspective of Civilian and Rebel agents:

� Mass protest, in which a larger volume of Civilianagents (5,000 instead of 1,000) was introduced. Thisprovided ingredients for a protest riot (Earl, Soule,and Mccarthy 2003; McCarthy, Martin, and McPhail2007).

� Angry mob, in which 1,000 hyperaggrieved Civil-ian agents (i.e., possessing higher initial values forgrievance; see Table 1) were introduced to the sim-ulated space. This provided opportunities to experi-ment with dynamics of food riots (Taylor 1996).

The third collection of scenarios portrayed crowddynamics from the perspective of Police agents:

� Nonengagement, in which fifty Police agents were mo-bilized to supervise a crowd of Civilian and Rebelagents but were under instructions not to arrest any-body (although the Civilian and Rebel agents didnot know this). This allowed us to experiment withthe influence of Police on crowd perception (Pratiand Pietrantoni 2009).

� Riot police, in which a 200-strong squad of Policeagents was deployed to the riotous crowd, as a force-in-numbers (Waddington 1991), in addition to their

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Table 1. Varying parameterization of the model to produce different simulation scenarios

Simulation scenario

Variable Base Built environment Riot police Mass protest Angry mob Nonengagement

Simulation run time 12 hours 12 hours 12 hours 12 hours 12 hours 12 hoursLegitimacy 0.82 0.82 0.82 0.82 0.25 0.82Maximum jail term 24 hours 24 hours 24 hours 24 hours 24 hours 0 hoursCivilian and Rebel vision (m) 7 7 7 7 7 7Police vision (m) 7 7 7 7 7 7Number of Police 50 15 200 50 50 50Number of citizen agents 1,000 285 1,000 5,000 1,000 1,000Rebel WPolice –0.5 –0.5 –0.5 –0.5 –0.1 –0.5Rebel WCivilian 0.5 0.5 0.5 0.5 0.9 0.5Rebel λ 0.5 0.5 0.5 0.5 0.11 0.5Police WRebel 0.5 0.5 0.5 0.5 0.5 0.5Police WCivilian 0.5 0.5 0.5 0.5 0.5 0.5Police µ 1 1 1 1 1 1Arrest distance (m) 2 2 2 2 2 2Is jail a deterrent? Yes Yes Yes Yes Yes NoAgent field of vision 120◦ 120◦ 120◦ 120◦ 120◦ 120◦

Patch length per agent step (m) 0.25 0.25 0.25 0.25 0.25 0.25Distance buffer (m) 0.5 1.25 1.25 1.25 1.25 1.25Infrastructure obstacles? No Yes No No No No

default behavior. This provided the seeds for a policeriot (R. Stark 1972).

The fourth set of scenarios was designed to explorethe interplay between varying tactics and strategies foragents (Table 2):

� Equal treatment, in which Rebel agents were equallydisposed to pursuing Civilian agents and avoidingPolice agents, and Police agents gave equal prefer-ence to chasing Rebel agents and protecting Civil-ian agents. This tested the balance between opposingforces of control in the crowd (this is the base sce-nario already described).

� Police pursue Rebels, in which Rebel agents balancedtheir preferences for fleeing from Police agents andpursuing Civilian agents to recruit, but Police agentsweighted their behavior strongly in favor of pursuingRebel agents, with a comparatively weak impulsetoward Civilian agents. This created an enforcementrole for police.

� Police protect Civilians, in which the preceding sit-uation was reversed: Police agents weighted theirbehavior strongly toward protecting Civilian agentsat the expense of a weakened impulse for chasingRebel agents to arrest. This placed Police in a pro-tective role.

� Rebels recruit Civilians, in which Police agentsadopted equal affective propensity toward Rebel andCivilian agents, but Rebel agents weighted their be-havior strongly in favor of seeking out Civilians torecruit to the cause, ceding most of their desire toevade capture by the Police. This rendered riotersrelatively active in expanding further rioting.

� Rebels avoid Police, in which the Police adopted abalanced strategy again, but Rebel agents favoredavoiding Police over recruiting Civilian agents. Inessence, this characterized rioters as relatively risk-averse.

� Battle for Civilians, in which the Police agentsstrongly weighted their behavior toward protectingand recruiting Civilian agents and the Rebel agentsemphasized recruitment of Civilian agents to the riot.

� Cat and mouse, in which Rebel agents were stronglyweighted toward avoiding Police, whereas the Policewere strongly weighted toward capturing them.

In all model runs, agents’ bodies were representedwith circular area of 0.1419 m2, which provided a real-istic physical footprint on the ground and a small bufferto account for ambulation of their limbs (Fruin 1971).We were most interested in rather small-area spatio-temporal dynamics, so agents were placed in a squarefield space of ∼4 km2 in area in most of the scenariosand their activity was tracked on the order of seconds.

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Table 2. Varying parameterization of the model to produce varying behavioral strategies for agents in simulation

Strategies

VariableEqual

treatmentPolice pursue

rebelsPolice protect

civiliansRebels recruit

civiliansRebels avoid

policeBattle forcivilians

Cat andmouse

Simulation run time 12 hours 12 hours 12 hours 12 hours 12 hours 12 hours 12 hoursLegitimacy 0.82 0.82 0.82 0.82 0.82 0.82 0.82Maximum jail term 24 hours 24 hours 24 hours 24 hours 24 hours 24 hours 24 hoursCivilian and Rebel vision (m) 7 7 7 7 7 7 7Police vision (cells/m) 7 7 7 7 7 7 7Number of Police 50 50 50 50 50 50 50Number of citizen agents 1,000 1,000 1,000 1,000 1,000 1,000 1,000Rebel WPolice –0.5 –0.5 –0.5 –0.3 –0.7 –0.3 –0.7Rebel WCivilian 0.5 0.5 0.5 0.7 0.3 0.7 0.3Rebel λ 1 1 1 0.43 2.33 0.43 2.33Police WRebel 0.5 0.7 0.3 0.5 0.5 0.3 0.7Police WCivilian 0.5 0.3 0.7 0.5 0.5 0.7 0.3Police µ 1 2.33 0.43 1 1 0.43 2.33Arrest distance (m) 2 2 2 2 2 2 2Is jail a deterrent? Yes Yes Yes Yes Yes Yes YesAgent field of vision 120◦ 120◦ 120◦ 120◦ 120◦ 120◦ 120◦

Patch length per agent step (m) 0.25 0.25 0.25 0.25 0.25 0.25 0.25Distance buffer (m) 0.5 0.5 0.5 0.5 0.5 0.5 0.5Infrastructure obstacles? No No No No No No No

This field space was designed as a torus for the sake oftractability in simulation, although only a small frac-tion of total agents interacted on the borders. (Thebuilt environment scenario was constrained to 303 m2

in area and agents were confined within its bounds.)We should note that the model can accept largerspaces and any two-dimensional configuration of builtenvironment.

Results

We examined the outcomes of the simulation sce-narios using several vantages. First, we wanted to testwhether the model could generate realistic geographicbehaviors within crowds, as this is underdeveloped inexisting models. The second concern was for complex-ity and the model’s ability to produce novel behaviorsthrough complex adaptation—what might, arguably,be termed as emergence—and whether it could gener-ate qualitatively complex signatures (J. Epstein 1999).The third evaluation property relates to the usefulnessof the model in supporting theoretical inquiry aboutrioting.

In what follows, the results of each of the scenariosmentioned in the previous section are presented in thecontext of the four criteria we have just described. Eachsimulation scenario was run ninety-nine times and we

report averaged results to reduce the potential influenceof artifacts from initial (random) positioning of agentsat the start of a simulation run. Each individual modelrun generated 43.2 million data points. Running eachscenario yielded a total of ∼4.28 billion data points.

Base Scenarios

The base parameterization provided a mixed riotscenario, containing elements of food riots, protestriots, police riots, and hooliganism. Under this scenariothe crowd phased quickly from a heterogeneous state,to collective agitation (Figure 5A), then to protest enmasse with ∼20 percent of the crowd joining the riotat its peak after one hour (Table 3). There was a sharpincrease in rioting early in the simulation, as thoseindividuals who were already aggrieved began to act outand this outward manifestation spread (as information)through the crowd at large. The police responded byarresting rioters, but it took some time to make muchdifference (∼1.25 hours). After seven hours, the policegained full control, but only after widespread arrest(∼40 percent of the crowd). As rioters were jailed andwere removed from the crowd, there were fewer freeagents to catalyze further rioting and the crowd shiftedphase back to a quiescent (outward) state that lockedin thereafter, although many of the citizens might stillhave felt (internal) hardship.

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Figure 5. (A) The base scenario for the model (agents are endowed with default parameter values and seeded in a plaza-type space). In eachof the line plots that follow, results are reported as averages of ninety-nine runs of the simulation with varying seed locations for agents atthe initial time step. (B) Agent dynamics in the built environment scenario, in which agents are equipped with default parameter values andplaced in a streetscape with urban infrastructure. (C) Agent dynamics in the angry mob scenario, in which the crowd’s feeling of legitimacytoward authority is reduced to 0.25. (D) Agent dynamics in the mass protest scenario, in which the number of crowd participants is increasedto 5,000. (E) Crowd dynamics under the riot police scenario. (F) Crowd dynamics under the nonengagement scenario.

We evaluated the extent to which like-minded (ri-oting or nonrioting) agents tended to collocate, by cal-culating a global (i.e., one value for the entire fieldspace, per time step) Moran’s I statistic for spatialautocorrelation (−1 < I < +1; Moran 1950) for ev-ery second of the simulation over the first hour (afterwhich volatility diminished; Figure 6). Citizen agentsshowed a weak tendency for positive spatial autocor-relation in activity: Globally, agents tended to clus-

ter in areas with high volumes of rioters or areas withhigh volumes of nonrioters. In other words, the crowdpolarized through self-organization from initially het-erogeneous conditions. This micro-to-macro, mass self-organization resembles end states of other complex so-cial models (Sakoda 1971; Schelling 1971), but we canalso consider its dynamics. Autocorrelation increasedrapidly in the early part of the riot and fluctuatedthereafter.

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Table 3. Qualitative model results

Benchmark

ScenariosTiming of riot

peakCrowd involvement

at peak (%) Riot duration Peak durationTiming of

restored control

Proportion ofcrowd arrested

(%)

Base 70 minutes 20 6 hours 70 minutes Hour 7 45Built environment 10 minutes 10 2 hours 25 minutes Hour 2 42Riot police 60 minutes 5 9 hours 3 hours Hour 10 45Mass protest 90 minutes 10 8 hours 4 hours Hour 11 45Angry mob 60 minutes 55 11 hours+ 60 minutes Never 79Nonengagement 12 hours 27 11 hours+ 11 hours+ Never None

StrategiesEqual treatment 70 minutes 20 6 hours 70 minutes Hour 7 45Police pursue Rebels 45 minutes 17 5.25 hours 60 minutes Hour 7 42Police protect Civilians 60 minutes 20 6 hours 90 minutes Hour 7 42Rebels recruit Civilians 60 minutes 20 5 hours 60 minutes Hour 6 42Rebels avoid Police 60 minutes 19 6.5 hours 75 minutes Hour 8 45Battle for Civilians 65 minutes 20 7 hours 75 minutes Hour 8 45Cat and mouse 50 minutes 14 3.5 hours 75 minutes Hour 4.5 45

We can zoom in on the results to evaluate local(space–time) patterns of behavior at the scale of in-dividual agents. This is useful in illustrating how agentsuse their geographic abilities and how they interact insimulation. For example, Figure 7 illustrates how riot-

ing agents were successful in avoiding law enforcementin some areas, because they saw the police coming andwere able to veer and run away. In other areas, theywere less successful and resorted to deceptive behaviorby dialing-down outward signs of rioting or physically

Figure 6. Global spatial clustering of agents of like state-values in the base scenario. Values of zero indicate no statistically significantclustering, positive values indicate positive spatial autocorrelation, and negative values indicate negative spatial autocorrelation. After fifteenminutes of rioting (900 seconds), citizen agents begin to cluster into areas where there are low counts of nearby rebels and areas where thereare high counts of nearby rebels (I ∼= +0.25 ± 0.07) and they sustain this pattern for a further forty-five minutes. Agents show no evidenceof global clustering based on hardship or net risk.

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Figure 7. In this illustration, the space–time paths of a subset of the rioting crowd are shown in a portion of the simulated area. This figurecorresponds with the first hour of the simulation portrayed in Figure 5A; X and Z are two dimensions of space; t is a temporal dimension. Localhotspots and cool spots of riotous activity are evident in the space–time movement of individuals in the crowd. Areas that Police cover wellremain quiet; those that they miss are relatively active in rebellion. (Color figure available online.)

avoiding police to escape apprehension. Figure 7 alsoshows the police usefully employing their spatial abil-ities to evaluate the crowd and to identify, chase, andapprehend rioters.

Riot dynamics in the built environment scenariowere dramatically different because of the reduced num-bers of participants and the effect of the built environ-ment on agent vision and movement (Figures 5B and8). The riot was comparatively unsuccessful and short-lived; agents were relatively easily chased and appre-hended when identified by the Police.

Civilian and Rebel Scenarios

The angry mob scenario was designed to examinefood riots (Taylor 1996), in which individuals havebeen building their animosity for some time ahead of as-sembling in a crowd to demonstrate mass grievance. To

represent this, we seeded agents with lowered feelingsof legitimacy (0.25) instead of the base value (0.82).The resulting dynamics differed significantly from thebase scenario (Figure 5C). The initial phase shift towardrioting was dramatic, with 55 percent of the crowd get-ting involved at its peak. The police responded quickly,arresting a huge portion of the rioting crowd. Comparedto the base scenario, the decline in rioting and movetoward quiescence was relatively sharp, largely becausethe arrest rate was high. The police had to arrest 80percent of the crowd before gaining full control.

The mass protest scenario was designed to mimic thesorts of dynamics that might permit rioting to breakout in a very large (5,000 agents) and otherwise law-abiding crowd, as might occur, for example, during apolitical rally (Gillham and Marx 2000). The resultswere quite close to the base scenario, despite the influxof a larger volume of participants (Figure 5D), and the

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reasons for this are quite interesting. The rebellion wassomewhat slower to take hold, but it was longer lasting(∼2.5 hours) than in the base scenario (which lasted∼1.25 hours). The civilian crowd was much larger inthe protest scenario and even though there were moreaggrieved agents to catalyze a riot, there were also agreater number of riot-averse agents to dampen thosetendencies. In essence, this provided a natural, self-organized control mechanism within the crowd itself(Russell, Arms, and Mustonen 1999).

We analyzed the mass protest scenario for local spa-tial autocorrelation, using a local Moran’s I statistic(Anselin 1995) on agents’ arrest likelihood. The resultsare shown in Figure 9, against a backdrop illustratinga kernel density–smoothed (Oliver and Webster 1990)surface of citizen-agent grievance levels per time step.In the early stages of the simulation, agents were seento form statistically significant (at a 99.9 percent con-fidence interval) local clusters: Agents with low arrestlikelihoods clustered together in space and time (withstatistically significant geography). These low–low clus-ters contained relatively high grievance levels and weremostly outside the attention of the small police force onthe scene. This shows the model working appropriately;the Police only responded to Civilian agents’ outwardsigns of rioting. Small clusters of agents with high arrestlikelihoods were also visible, next to Police; the Po-lice performed a relatively good job of identifying localoutbreaks of rioting and moved to target them. Once alarge-scale riot had taken hold, a few clusters of agentswith low arrest likelihoods appeared, which the Policewere able to efficiently guard. By the second hour, areasof the space that were well patrolled by Police exhibitedrelatively low grievance among citizens. By the eleventhhour, few riotous clusters remained, and although it stilldemonstrated relatively minor levels of grievance, thecrowd remained under relative control. The Police stillneeded to patrol some previous hotspots, however, toensure that the crowd did not revert to rioting.

Police Scenarios

The scenarios designed to test police behavior incrowd insurrection events produced significantly differ-ent dynamics, compared to the base scenario (Table 3).In the riot police scenario, 200 police were deployed tothe crowd (an increase from fifty in the base scenario),providing a force-in-numbers response (Waddington1991). As a result, the riot never really took off. Theinitial onset took hold with only a small minority of thecrowd, ∼5 percent (Figure 5E; Table 3). Just as rioting

began to spread, the Police (in larger numbers and ableto cover more ground) quickly imposed order, initiallywith a handful of arrests.

Under the nonengagement scenario, Police patrolledthe simulated space, without interacting with rioters,but still influencing the actions of Civilians and Rebelsthat they passed. In essence, this represented preven-tative policing (Waddington 1991). When the Policesaw rioters, they still chased them, but they did notarrest them. This had the effect of dampening over-all rioting in the crowd, but the riot, once underway,was long-lasting and persistent (Figure 5F). The Policemaintained relative order but never fully gained con-trol. They did, however, avoid mass arrest.

The Influence of Strategy and Tactics

Deploying spatial weights on agents’ perception, cog-nition, and movement allowed us to study the influ-ence of geographical tactics and strategies. The equaltreatment strategy is the same as the base scenario al-ready discussed and Rebels and Police were balanced intheir affective biases (Table 3).

Police-Oriented Strategies. Two police strategieswere explored. The Police invested the majority of theireffort in protecting the civilian population from riot-ers in the Police protect Civilians scenario. (Rebelsadopted default weighting, balanced in their preferenceto avoid the Police and chase Civilians.) This strategywas less successful for the Police than the base scenario:The riot peaked earlier, the peak was sustained longer,and the riot lasted longer than under the equal treat-ment strategy (Table 3).

Under the Police pursue Rebels strategy, the Policewere designed to be more aggressive in pursuingrioters than they were in protecting nonrioters. Thisproved to be only slightly more useful for the Policein maintaining order. The initial shift to riot occurredearlier than in the equal treatment strategy, likelybecause the Police were less concerned with protectingCivilians; this left the crowd freedom (and space) toriot. The Police gained the upper hand quickly, how-ever, and they limited rioting to five hours (comparedto seven hours in the base scenario). As with the equaltreatment strategy, full control was achieved by hourseven and the Police had to jail a large proportion ofthe crowd to achieve it (Table 3).

Rebel-Oriented Strategies. Two strategies weredesigned to study the influence of sedition. (Weightsfor Police were kept at the default, balanced between

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Figure 8. The position of the crowd after one hour of the built environment scenario. The crowd is reduced from fifty to fifteen Policeagents and from 1,000 to 285 non-Police agents for the built environment scenario. For illustration purposes only, Jailed agents are shown atthe location where they were arrested; Jailed agents are removed from the space immediately on apprehension in simulation. (Color figureavailable online.)

chasing rioters and protecting nonrioters.) Under theRebels recruit Civilians strategy, Rebels were biasedtoward pursuing Civilians in a bid to further fomentrioting (at the expense of avoiding apprehension by thePolice). This strategy was not particularly effective forthe Rebels: They did not recruit more Civilians thanthey would have under the equal treatment strategy andthey did not evade capture particularly well (Table 3).The Rebels sought out new recruits, but in doing so theyexposed themselves to arrest.

Under the Rebels avoid Police strategy, riotousagents adopted covert behavior, still seeking out newrecruits but avoiding the Police more strongly than inthe equal treatment strategy. This was slightly more ef-fective for the Rebels, particularly in the early stages ofthe riot: They reached peak rioting sooner than in thebase strategy and they managed to sustain the riot foran extra hour (Table 3). To some extent, the cards arealways stacked against the Rebels, as the Police can re-move them from the riot. The Rebels, of course, cannot

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Figure 9. (A) Local surfaces of agent emotion (grievance) are calculated for the mass protest scenario. Local measures of spatial autocorrelationare used to extract statistically significant hotspots (high–high spatial autocorrelation) and cool spots (low–low spatial autocorrelation) ofclustering based on likelihood of arrest for (B) hour one, (C) hour two, (D) hour four, and (E) hour eleven of the simulation. (F) Space–timepaths for the first eleven hours of Police movement show the concentration of their patrols in the portion of the space with the greatestclustering of rebellion, although islands of initial outbreak must also be patrolled to keep them from reverting to riotous activity. (Color figureavailable online.)

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oust Police. This is a realistic depiction of the relativepower balance in riotous crowds.

Conflicting Strategies. The two final strategic sce-narios were designed to explore crowd dynamics underconflicting strategies between Police and Rebels. Underthe battle for civilians strategy, both Rebels and Policeadopted strategic behavior to seek out nonrioters inthe crowd. In the case of the Police, their motive wasto protect Civilians, whereas the Rebels tried to recruitCivilians to riot. This strategy was only slightly less suc-cessful for the Rebels than the base strategy (Table 3).

Under the cat-and-mouse strategy, the Police andRebels devoted the majority of their attention to eachother, paying comparatively little attention to theCivilian population (except that Rebels could losethemselves in nonrioting portions of the crowd to avoiddetection). The Police and Rebels essentially played agame of chase under this scenario. The Police playedthe game very well and the results were relatively disas-trous for the Rebels. The Rebels only catalyzed a smallriot, which halted quite quickly. The Police managedto restore full order within 4.5 hours (Table 3).

Conclusions

Riots are difficult to experiment with tangibly or us-ing standard social science analyses. One alternativemight be to use modeling and simulation to explore riotssynthetically. Several riot models have been developed,but existing approaches have emphasized abstract rep-resentation of riot phenomena and processes that limitthe range of questions that can be posed in simulation.We have presented an alternative scheme that expandsthe abilities of models to synthesize riots by using apolyspatial, agent-based architecture that can accom-modate rich behavioral detail at process scales from theindividual to the crowd. We believe that this approachis quite novel and useful.

Methodological Innovation

Our scheme introduces significant methodologicalinnovation. Our attention to detail is much more care-ful than in standard approaches, so that a richer set ofprocess dynamics can be represented, at the character-istic and atomic timing and spacing of riot phenomena.This allows us to better tailor simulations to real-worldscenarios and it facilitates a wider range of inquirywith the model than is usually achieved in existing,abstract approaches. This achievement is important:

Many agent-based models advertise their ability to mapindividuals to macro-outcomes, but coarse and abstractrepresentation of behavioral agency is usually the norm.Many agent-based models simply use existing macro-equations on agents (Batty and Torrens 2005). Thisrather defeats the purpose of building individual-basedmodels and it has led many authors to rightfully crit-icize the methodology quite consistently (Faith 1998;Torrens and O’Sullivan 2001; Couclelis 2002; Clifford2008), but very little is commonly done to challengethis critique. Our approach is distinct: We embrace de-tailed behavior in simulation.

Another long-standing problem with agent-basedmodels is the prevalence of anemic geographic func-tionality (Torrens 2010a). Geography is generallyconsidered as an afterthought, with spatial dynamicsimplied from visual output, despite the fact thatgeography might have received only cursory treat-ment in the actual model (J. Epstein 2002). This issurprising, as agent-based models can support rathersophisticated geographical algorithms and processes(Benenson and Torrens 2004). Although there is arather consistent dialogue in the theoretical literatureabout the significance of geography in riot dynamics,our model is among the first serious attempts to tacklegeography in riot simulation. This alone is novel and,as we discuss later, it turns out to be quite valuable.

Our approach can also extend (and deepen) exist-ing socioemotional agency with geographic wrappersthat provide added geographic functionality (vision,steering, movement, neighbor inquiry, vector resolu-tion, collision detection and avoidance, affective bi-asing) and second-order space–time processes (spatialinteraction, diffusion, scaling, clustering, segregation,polarization, chasing, and avoidance). We achieved thisin a way that retained existing social agency faithfullybut enabled it spatially. This sort of model docking isa topic of avid interest in the agent-based simulationcommunity (Torrens and Benenson 2005; Rank 2010);although this is not the central topic of this article, ourexample does show how such docking can be achievedfor computational social science applications.

We embedded the modeling and simulation compo-nents of the work in a unified pipeline that also in-cluded spatial analysis, spatial statistics, geostatistics,and geovisualization for sweeping the parameter spaceand results of simulations. This goes far beyond the usualapproach, which relies on simple plots of model param-eters over time and descriptive multivariate statistics.Standard approaches usually lack potency anyway, be-cause coarse, aggregate measures are commonly used to

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examine individually specified models. In a sense, thismuddies much of the underlying detail, unless macro-outcomes are known a priori and deliberately sought outin analysis (which is difficult for riot simulation, wherethe whole point of modeling is to seek out such thingsin the first place).

Substantive Findings

We touted the potential advantages of our model asan experimental laboratory for studying rioting. So itis fair to ask what we actually learned about rioting insimulation.

The Role of Geography. A long-standing critiqueof agent-based modeling centers on “unwrapping” (Hol-land 1995, 137)—the practice of building results di-rectly into model design only to rediscover them in sim-ulation. We deliberately built geographic features intoour model but to provide the functionality for dynamicinterplay of the features in simulation. This is differentthan baking in outcomes. Any substantive findings thatthe model generates are therefore authentic (within theparameters of the simulation).

The processes that drive riotous crowds are some-times distinct at different scales, and our model showshow they can connect, inexorably, through geography.Theory suggests—and our simulations show—that theactions of a handful of individuals can, in some condi-tions, shape the dynamics of an entire crowd, whereasin others the actions of the few are diluted by thoseof the many. Our model allows processes to jump scalebarriers, because the agents that create and propagatethose processes are polyspatial. In particular, they canreact to information channels at diverse scales. For somesituations, scaling allows individuals to be teased intorioting under the perceived protection of the group atlocal geographies. In the reverse direction, seditious be-havior at local geography or at an individual level canbe dampened by ambient quiescence in a large crowd.Temporal scaling is also important to understandingrioting. A charged crowd can shift phases from rela-tive quiescence to sedition in just a few minutes. Oursimulations show how small changes in initial condi-tions and behavior catalyze these shifts dynamically.The ability of agents to dip into and process informa-tion (whether real, imagined, or wrong) at differentscales provides the mechanics for emergence, feedback,self-organization, and allometry. This implies that spa-tially nonmodifiable units on which the finest scale ofthe simulation is built (and their assembly into coarser

process building blocks) are critical in representing riotsappropriately, as is their assembly into coarser buildingblocks for riot processes. Ideally, atoms would representindividuals and would facilitate construction of real-istic behavior that allows them to bridge scales. Thisseems difficult to achieve without realistic treatment ofgeographic behavior.

This leads us then to the role of geographic behaviorin determining rioting. By representing behavior explic-itly (not abstractly), our model can show how agents’use of geographic information and their spatial think-ing can shape riot dynamics. We have demonstratedthis specifically by playing with different configurationsof characteristics and strategies. By giving agents geo-graphic behavior, agency becomes less viscous in crowddynamics than it might without, because agency is mo-bilized and interpreted in, or exposed to, different times,places, contexts, and company. Mobility also allows theconduits for information exchange between simulatedentities to shift and change form, as can the inputsto individual agents’ mental maps. Here, there are ob-vious parallels with the real world, where informationexchange courses through crowds rapidly, differentially,and dynamically. Agents need to be mobile—in theiractivities, actions, reactions, and interactions—to berealistic in riot models. These dynamics are difficult torepresent authentically in cell-based models that rely onabstract movement proxies. In CA, for example, agentcells must languish in situ and wait for information tofind them and wash over them, rather than proactivelyseeking out (or avoiding) information in the environ-ment (Torrens 2010a). There are other pitfalls in re-lying on proxies of movement, in particular, becauseobserved effects in models could derive from artifactsof the proxy, rather than having an analog in theoryor real-world phenomena. This problem has been doc-umented for computational automata (Faith 1998) butis perhaps relevant across much of computational socialscience, as others have noted (J. Epstein 2007).

Physical geography is also significant. Moving acrowd from an open plaza setting to a walled (urban)space had dramatic effects, because it altered the sup-ply of information to agents’ geographic behavior. Ourexperiments with built environments were relativelyabstract and the topic warrants further investigation,particularly into the extent to which physical and hu-man geography codetermine riot dynamics.

Exploring Existing Riot Theory in Silico. Ourmain preoccupation in modeling was with geographicbehavior, but we included several popular social science

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theories of rioting in our model, which we can hesitantlyexamine. For example, we considered threshold modelsfor collective behavior. The threshold theory suggeststhat a domino or bandwagon effect might explain thespread of riotous activity within a crowd (Granovetter1978), that once some target level of participation hasbeen reached, people who would otherwise feel hesi-tant to act out might feel free to do so because thecollective costs of their actions are reduced in aggre-gate. We built thresholds directly into the individualbehavior of our agents by specifying legitimacy andhardship states per agent. The geographic behavior ofagents then allowed thresholds to be animated locallythrough the activation rule and subsequently propelledat a distance by secondary geographic processes. Undercertain scenarios and strategies, Rebel agents’ proac-tive geographic behavior also allowed them to seek outnonrioters to seduce to the riot, which could catalyzeor maintain some locally safe threshold for acting out.In this way, then, agents put the threshold model intoproactive use. This differs considerably from Granovet-ter’s (1978) original probabilistic/equilibrium formula-tion of the idea, as well as subsequent mathematicalimplementations (Granovetter and Soong 1983). Theimplications of this extension to the threshold modelare significant. A much richer understanding of the gen-esis and formation and propagation of threshold effectscan be garnered within the crowd. This understandingis distinct from the sorts of explanations usually used toaccount for generated macrostructures, which are com-monly attributed to abstract notions of emergence (seeJ. Epstein 2002, or even Schelling 1971). In contrast,our formulation shows how threshold effects can gener-ate local (or macroscale) clusters that bubble up, merge,starve for new recruits, expand, disappear and reappearin space and time, and so on. In essence, the thresholdphenomenon is much more fluid because the effect isgeographic.

The role of information is discussed prominently inthe literature (Wright 1978; McPhail and Wohlstein1983; Rheingold 2002), but it is rarely treated in mod-els. Our simulations show that information is critical indetermining interactions within crowds and we are ableto show how information exchange can influence thelarger crowd mosaic. Our scenarios demonstrate howthe trade of nonverbal information can alter riot dy-namics, for example, through outward expression (e.g.,grievance), locomotion (police chasing bellicose riot-ers), or spatial interaction (clustering and colocationin space and time). These examples are important inshowing how geography can foster dynamism in infor-

mation. Some effects in crowds might start out as non-spatial but might become mobilized by diffusion (e.g.,affect); some might be explicitly geographical (e.g.,locomotion); and others might play out through dy-namically malleable and scalable space–time structures(e.g., clusters). Our simulations show that the qual-ity of information is also important. Individual agentsoften have incomplete access to information, particu-larly in densely packed crowds where their informationmight be limited to small-scale shifts in immediate con-ditions around them, and their spatial cognition mightbe bounded. Misinformation could be equally impor-tant. Seditious actors in a crowd might seek to delib-erately manipulate the flow (a geographic process) ofinformation to their needs (Prentice-Dunn and Rogers1982), as when rioting agents in our simulations turnedto deception near police. The police can similarly in-tervene in information exchange through the crowd, byfalsely projecting force, for example.

The role of collective behavior in riotous crowdsis also a significant subject in the theoretical liter-ature (McPhail and Wohlstein 1983). Although ouragents deployed strategies to determine their interac-tions relative to each other in simulation, they werenot given explicit rules for collaboration; that is, eachagent within a given role acted independently. Yet, col-lective space–time patterns did emerge in simulation,with clearly forming hotspots and cool spots of activity(and emotion), for example. There is perhaps a peda-gogical lesson here: Much collective behavior can behappenstance, a product of a natural sorting and shuf-fling of the crowd. As other researchers have shown, thiscan happen even with small impulses amid a handful oflocal interactions (Schelling 1971).

The idea of a crowd mentality is a controversial hy-pothesis that is sometimes discussed when consideringrioting: the notion that a riotous crowd might act withsome sort of pack-like behavior, ceding their individu-ality to a collective norm. Although it has long beenunderstood to be erroneous (Couch 1968), the ideastill persists (Schweingruber and Wohlstein 2005). Ourmodel can help to explain why the notion of crowdmentality is problematic. Interpretation is one reason:Descriptive plots of riot dynamics (Figure 5) might im-ply homogeneity in the crowd, but spatial analysis showsthat heterogeneous geographies of clustering manifestbeneath this aggregate pattern. This is what McPhail(2008) has referred to as the “crowd as patchwork.”Even when agents in our scenarios were seeded withthe same initial parameters and transition rules, the in-formational ingredients to their decision making were

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variable because they were polled from local surround-ings, which were constantly in a state of spatiotempo-ral flux (because agents moved, others moved aroundthem, or information metamorphosed as it spread). Inessence, the informational currency for interaction be-tween crowd members is always changing and so, evenwhen given similar predispositions, behavioral responseis not fixed in space or time (Granovetter 1978).

Ideas about complexity permeate all of thesediscussions. Because riots scale from individualaction–reaction dynamics to (and within) the largersocial and built substrate of the ambient environment,they often manifest as complex adaptive systems. In-deed, we identified some signature characteristics ofcomplex systems in our simulations: emergence, self-organization, phase shifts, positive (escalation) andnegative feedback (calming), and path dependency.Clearly, understanding the complex adaptive propertiesof riots is important in understanding the phenomenon.This is a topic that has not received much attention inthe literature, even though it is actively studied for othercrowd phenomena (Vicsek 2003).

To the extent that our model can be relied on as a suf-ficient analog for riots in the real world (and we makeno warranties in this regard; we consider the modelas a computational laboratory for testing phenomenain which ground truth that might “verify” the model’smatch to a particular riot is almost impossible to attain),the scenarios that we simulated provide some practicallessons for managing riotous crowds. The various strate-gic scenarios for policing show, for example, that a masspolice presence might be counterproductive to calm-ing potential sedition (Waddington 1991). Also, policecan project force quite effectively without having toactually use force (Prati and Pietrantoni 2009). Also,recognizing shifting patterns in the information that acrowd exudes—particularly signatures of individual andcollective behavior in space and time—and reacting ap-propriately and in a timely manner could be useful inmanaging a crowd on the brink of sedition or calmingriotous crowds to more quiescent end states. Deliber-ately introducing, modifying, or blocking informationdiffusion could also be important.

Current Limitations and Future Avenues forResearch

Rioting is a highly variable phenomenon, with manypossible ingredients. Our model, like all models, is anabstraction of reality. We have strived to make it lessabstract than existing models, but some features are

missing. First, our portrayal of roles in rioting was lim-ited to four types of protagonists. This is useful in ex-amining some of the prevalent agencies considered inrioting, but it is perhaps stereotypical, representing as K.Epstein and Iveson (2009, 271) remarked, “a binary dis-tinction between the ‘virtuous’ urban citizen (in needof protection) and the ‘unruly’ protester (from whomthe virtuous citizens needed protection).” An extendedmodel could add additional agents: agent-provocateurs,hooligans, instigators, riot and nonriot police, and soon. There is nothing in the architecture of the modelthat prevents the addition of more agents or agency, butthis would be a time-consuming undertaking.

Second, our built environment scenario was quitesimplistic and did not fully reference the availablewisdom regarding rioters’ use of urban infrastructure(Newman 1972, 1996). The relationship betweenbehavioral geography and the built environment isthe topic of a separate thread of research that we areactively engaged in, and we hope to build bridgesbetween that work and our riot model in the future.

Third, we have not accounted for the role of socialnetworks in rioting. The connection between socialnetworks and space is a topic of relatively recent in-vestigation in the literature and relatively little workhas been done on this in computational social science(Butts 2009; Torrens 2010b). Dibble has made signif-icant inroads into exploring these issues (Dibble andFeldman 2004) but at a much coarser scale than ourmodel has considered. It is potentially a quite valu-able avenue for future inquiry and, again, our modelingframework does not preclude it from being incorporated.

Fourth, we could represent information moreexplicitly in the model, either through vocal exchangesbetween rioters and police in simulation or by modelingthe influence of mobile Internet and communicationstechnologies in riot dynamics (Rheingold 2002). Therole of body language and gait in crowd dynamics issomething that we are examining in other models wehave built, using full-body motion capture data, forexample (Figure 10). This would be of clear value(Scheflen 1972) if incorporated into the scheme thatwe introduced in this article.

Fifth, our pipeline presents an interactive toolkit forexperimenting with riot dynamics, but we are the mainbeneficiaries of its use. We could broaden the user baseto “serious gaming” (Barnes, Encarnacao, and Shaw2009) about rioting by other researchers, police, stu-dents, or other stakeholders, for example. We are de-veloping an immersive version of the model that allowsusers to control (and move) characters as avatars in

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Figure 10. A screen shot from a prototyped immersive version of our riot simulation. Users can “drop into” the riot as avatars and movethrough the environment to experience a simulated riot vicariously. (Color figure available online.)

simulation (Figure 10), but extending this for action-able decision support will take further work.

Sixth, we did not deal with riot precursors. Thesecould be added to our pipeline, however, in a metasim-ulation that would also include city-level dynamics.We have experimented with coupling agent-based mod-els and more systems-oriented simulation architectures(input–output models, equation-free modeling, coarseprojective integration, animation), but the sorts of mod-els required to simulate city-wide, neighborhood-level,or perhaps even national target selection would likelyrequire much more involved consideration, because ofthe large range of intrasystem interactions that couldserve as drivers (see work by DiPasquale and Glaeser[1998] on the economics of rioting, for example).

Seventh, we have largely sidestepped the issue of cal-ibrating or validating the model to known conditionson the ground, primarily because of the difficulties in ac-

quiring “knowns” that we outlined earlier. Our modelis informed by appropriate theory and this is actuallyquite innovative. Clearly, though, we need to do moreto match the model and simulations to reality. Or, alter-natively, the model could be used to “hindcast” aboutknown riot events, with the view of providing oppor-tunities for future lessons to be learned. This could beattempted with adequate data. Automata are almost in-finitely extensible (Turing 1936) and our scheme doesnot constrain the amount of reality that can be intro-duced to the model. Building that know-how is difficult,although we think that our model can help.

Acknowledgments

This material is based in part on work supportedby the National Science Foundation under grant num-bers 1002517, 0643322, and 0624208. Any opinions,

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findings, and conclusions or recommendations ex-pressed in this material are those of the authors anddo not necessarily reflect the views of the National Sci-ence Foundation. Many thanks to Atsushi Nara for hishelp in accelerating the calculation of multiple Moran’sI values.

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Modeling Geographic Behavior in Riotous Crowds · analysis. Fifth, rioting is often dangerous for...

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